A boundary Harnack principle for infinity-Laplacian and some related results.
A linear and weakly nonlinear equation of a beam: the boundary-value problem for free extremities and its periodic solutions
A mixed problem for a Boussinesq hyperbolic equation with integral condition.
A propagation theorem for a class of microfunctions
Let be a closed set of , whose conormai cones , , have locally empty intersection. We first show in §1 that , is a function. We then represent the n microfunctions of , , using cohomology groups of of degree 1. By the results of § 1-3, we are able to prove in §4 that the sections of , , satisfy the principle of the analytic continuation in the complex integral manifolds of , being a base for the linear hull of in ; in particular we get . When is a half space with -boundary,...
A rotation invariant differential equation for vector fields
A third-order nonlocal problem with nonlocal conditions.
A three-point boundary value problem with an integral condition for a third-order partial differential equation.
A use of the Laplace method in differential equations
Abstract boundary-value operators and their adjoints
An inhomogeneous Dirichlet problem for a non-hypoelliptic linear partial differential operator.
An -analogue of the Vishik-Eskin theory.
Boundary value problem for Fuchsian partial differential equations and reflection of singularities
Boundary value problem with integral conditions for a linear third-order equation.
Boundary value problems of linear elastostatics and hydrostatics on Lipschitz domains
Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations
In the present paper we study the unique solvability of two non-local boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations. The uniqueness of the solutions of the considered problems are proven by the “abc” method. Existence theorems for the solutions of these problems are proven by the method of integral equations. The obtained results can be used for studying local and non-local boundary-value problems for mixed-hyperbolic type equations...
Boundary-value problems of Hilbert type for linear p-areolar differential equations in the form
Continuation of analytic solutions of linear differential equations up to convex conical singularities
Exact Solutions of Nonlocal Pluriparabolic Problems
MSC 2010: 44A35, 44A40
Existence et prolongement des solutions holomorphes des équations aux dérivées partielles
Homogeneous two-point problem for PDE of the second order in time variable and infinite order in spatial variables
We prove that homogeneous problem for PDE of second order in time variable, and generally infinite order in spatial variables with local two-point conditions with respect to time variable, has only trivial solution in the case when the characteristic determinant of the problem is nonzero. In another, opposite case, we prove the existence of nontrivial solutions of the problem, and we propose a differential-symbol method of constructing them.